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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 22nd 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave added a tad more to the Properties-section at _[[Riemann zeta function]]_.

   have added a tad more to the Properties-section at Riemann zeta function.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 25th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added various further illuminating (hopefully) details to the proof [here](http://ncatlab.org/nlab/show/Riemann+zeta+function#RelationToThetaFunctions) of how the Riemann zeta function relates to the Jacobi theta function via adelic integration. (This is pretty neat, I find. I learned this from Ivan Fesenko. But I gather it is standard in the field. Is this explicitly already in Tate's thesis?)

   I have added various further illuminating (hopefully) details to the proof here of how the Riemann zeta function relates to the Jacobi theta function via adelic integration.

   (This is pretty neat, I find. I learned this from Ivan Fesenko. But I gather it is standard in the field. Is this explicitly already in Tate’s thesis?)

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeAug 25th 2014
   • (edited Aug 25th 2014)
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   Author: zskoda
   Format: MarkdownItex> Is this explicitly already in Tate’s thesis? Yes. Though he treats more general case of twisted zeta functions and you have to substitute the special case of the idelic character corresponding to the Riemann case. See also the Garrett's lectures at [[Iwasawa-Tate theory]] for some details for the several special cases like the Riemann and Dirichlet zeta functions.

   Is this explicitly already in Tate’s thesis?

   Yes. Though he treats more general case of twisted zeta functions and you have to substitute the special case of the idelic character corresponding to the Riemann case. See also the Garrett’s lectures at Iwasawa-Tate theory for some details for the several special cases like the Riemann and Dirichlet zeta functions.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 25th 2014
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   Author: Urs
   Format: MarkdownItexThanks. Those lecture notes [Garrett 11](http://ncatlab.org/nlab/show/Euler+product#Garrett11) are pretty useful as a review.

   Thanks. Those lecture notes Garrett 11 are pretty useful as a review.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJan 9th 2019
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   Author: Urs
   Format: MarkdownItexPreprint today by Yau et al., relating $p$-adic strings to the Riemann zeta function: * An Huang, Bogdan Stoica, [[Shing-Tung Yau]], _General relativity from $p$-adic strings_ ([arXiv:1901.02013](https://arxiv.org/abs/1901.02013)) <a href="https://ncatlab.org/nlab/revision/diff/Riemann+zeta+function/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemann+zeta+function/20">v20</a>, <a href="https://ncatlab.org/nlab/show/Riemann+zeta+function">current</a>

   Preprint today by Yau et al., relating $p$-adic strings to the Riemann zeta function:

   • An Huang, Bogdan Stoica, Shing-Tung Yau, General relativity from $p$-adic strings (arXiv:1901.02013)

   diff, v20, current

6. • CommentRowNumber6.
   • CommentAuthorTom Mainiero
   • CommentTimeNov 2nd 2024
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   Author: Tom Mainiero
   Format: MarkdownItexUpdate broken link. <a href="https://ncatlab.org/nlab/revision/diff/Riemann+zeta+function/23">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemann+zeta+function/23">v23</a>, <a href="https://ncatlab.org/nlab/show/Riemann+zeta+function">current</a>

   Update broken link.

   diff, v23, current